I am using the Finesse API endpoint /finesse/api/Users to get a list of agents and their states, but I am not able to see which of the server pair they are logged into. The user list and agent state is shared across the hosts. Is there a way to determine which agents are connected to which side?
In practice, Finesse seems to be Active/Active and users can log in directly to either side of a PG pair. This excerpt from the desktop client failover section of this document seems to support this: "the agent does not automatically reconnect to the failed server after it recovers but instead remains connected to the alternate server."
If it is Finesse with UCCE, it is Active/Active. If it is Finesse with UCCX, it is Active/Standby.
As far as your original question of how do you know which server an agent is connected to, the answer is you can't. Is there a reason why you would like to know this information? Finesse has been tested where the max number of agents are all logged in to the same node. Even though Finesse is Active/Active for UCCE, they are both connected to the same CTI connection, so that wouldn't make a difference.